Question

Find the ratio in which the line 2x + 3y - 5 = 0 divides the line segment joining the points (8,-9) and (2,1).

Answer 1

Answer:

Step-by-step explanation:

let the ratio be k : 1

x = 2k + 8/k+ 1

y = k - 9 / k + 1

putting in equation 2x + 3y = 5

4k + 8 + 3k - 27 = 5k + 5

7k - 19 = 5k + 5

2k = 24

k = 12

ratio = 1:12

hope it helps

Answer 2

A(8,-9) B(2,1)

let the line 2x+3y-5=0 intersect at P(x,y)

$p (x \: comma \: y) \\ = m1x2 + m2x1 + \div m1 + m2 \: \: \: comma \: m1 \times y2 + m2 \times y1 \div m1 + m2$

P(x,y)=m1(2)+m2×8÷m1+m2 ,

m1×1+m2×-9÷m1+m2

X =2m1+8m2÷m1+m2 ,Y= m1-9m2÷m1+m2

SUBS. THE VALUE OF X AND Y IN THE GIVEN EQUATION

2(2m1+8m2÷m1+m2)+3(m1-9m2÷m1+m2)-5=0

(4m1+16m2+3m1-27m2)÷m1+m2 =5

(7m1-11m2)=5m1+5m2

7m1-5m1=5m2+11m2

m1(7-5)=m2(5+11)

2m1=16m2

m1/m2=16/2

m1:m2=8:1 ratio

HOPE IT HELPS U

MARK AS BRAINLIST